The ocean and atmosphere are in constant motion. Powered by the Sun
and a rotating Earth, their interactionsplay a critical role in shaping weather and climate.
Natural variations in winds, currents, and ocean temperatures can temporarily
affect weather patterns. For example, an El Niño event may
develop when the trade winds diminish. The trade winds affect ocean travel both
today and in the past by aiding early explorers and merchants traveling from
Europe to the Americas. The trade
winds are a pattern of wind found in bands around Earth's equatorial
region. They are the prevailing winds in the tropics, blowing from the
high-pressure area in the horse latitudes towards the low-pressure area around
the Equator. The constancy of the trade winds makes them important phenomena to
study.

What causes these winds near the Equator and who developed
the concepts that explain them?

Lesson 2 will guide you through the history of scientists
such as George Hadley, Edmond Halley and Gaspard-Gustave
de Coriolis, who developed the early theories that explain the forces powering
the trade winds and their effect on ocean surface currents. Computer models,
found in this lesson, will help you understand these forces that influence the weather and climate that you experience everyday.

Photo: Trade Winds Blow Through San Juan

What
Do You Know?

Before
beginning this lesson is it helpful to learn how much information you already
know about the Coriolis force. A simple preconceptions survey has been created
for you to assess your prior knowledge.

1. Click
on the blue Quiz button below.

2. Take
the quiz

3. Submit
your responses online and they will be automatically scored.

4. Return
to this guide and begin your exploration of the Coriolis force.

Heated Fluid Circulation

What drives the Trade Winds?

Heating fluids like air or water from beneath can make a fluid
unstable. A warmed fluid becomes less dense and will rise opposite to the force
of gravity. The cooler fluid above will move to replace the rising warm fluid
and it will be warmed itself. This cycle repeats to mix the fluid. The process
of convection describes motions in a fluid that result in the transport and mixing
of the fluid properties. Suppose
you heat a container of water on a stove burner.

1. What sort of motion happens in
the water?

2. Why does this kind of water
motion occur?

3. Imagine now that you put the same
pot of water into an oven with a top broiler (heat source above the water
surface). How would you expect the water to move?

4. Suppose you were asked to make a
prediction about how water temperature in the ocean varies with the depth of
the water. Which model – pot heated from the bottom or from the top
– applies to the ocean? As you go deeper in the ocean, will the water
become cooler or warmer? What effect will the temperature of the surface water
have on the air above?

The Intertropical
Convergence Zone, or ITCZ, is the region that circles Earth. Notice the band of
bright white clouds in center of the image near the Equator, where the trade
winds of the Northern and Southern Hemispheres come together. The intense sun
and warm water of the Equator heats the air in the ITCZ, raising its humidity
and causing it to rise. As the air rises it cools, releasing theaccumulated moisture
in an almost perpetual series of thunderstorms. This image is a combination of
cloud data from NOAA’s Geostationary Operational Environmental Satellite
(GOES-11) and color land cover classification data.

The
name, trade winds, derives from the Old English ”trade”, meaning path or track.
The trade winds helped ensure that European sailing vessels, including those
that Columbus sailed, reached North American shores.

Edmond Halley (1656-1742), pictured on the left, correctly understood the role of the Sun
in atmospheric circulation. He reasoned that intense solar radiation heated the
air near the Equator and caused it to expand and rise up. This rising air is
replaced by cooler air converging on the Equator from the northern and southern
hemispheres. Circulation of the air is driven by a pressure-gradient force,
which causes high-pressure (cooler, more dense) air to move into regions of
low-pressure (warmer, less dense) air. Under static conditions, fluids reach
equilibrium when pressure is the same at each depth. His theory predicted a
flow of air from the poles to the Equator where the air masses converge. But
the explanation does not account for the steady westward flow.

George Hadley (1685-1768), was an
English lawyer and amateur meteorologist, who first recognized the reason the
trade winds, preferentially blow westward. His explanation depended on the fact
that Earth is a rotating sphere and that sites on the surface of rotating
sphere travel with different speeds (travel different distances in equal
times).

Hadley
earned fame by realizing that Earth's rotation played a crucial role in the
direction taken by a moving airmass. He provided a description of the equatorial trade winds
that was essentially correct.

Weather,
which describes the current state of the atmosphere, normally fluctuates daily
due to a complex interplay of forces and processes. Any steady or cyclic
weather phenomena could be the result a dominating process.

These
phenomena provide opportunities to test
scientific models and hypotheses. In the
following pages you will work with the
equations that help us understand how
objects and air masses move on a rotating
sphere.

IllustrationCredit:
Tinka Sloss, New Media Studio, Inc.

Traveling On A Rotating Sphere

How Did Coriolis Use Math To Understand The Movement Of Objects
on a Rotating Sphere?

Gaspard-Gustave de Coriolis (1792-1843), pictured on the right, a
French mathematician, mechanical engineer, and scientist, worked out the
general formulas for motion of objects measured from rotating systems of
coordinates. Coriolis was able to determine the following simple rules for the
direction of moving objects on the surface of a rotating sphere, now known as
the Coriolis effect:

• The apparent force
(or Coriolis force) on moving objects on a rotating sphere is perpendicular to
the velocity of the object and the rotation axis.

• A balance of
forces cause objects traveling in the Southern Hemisphere curve to the left.

5. Consider the speed at which Earth
rotates at different locations. Click to see an animation of the Rotating Earth during the course of one day.
Locate the following sites: a marked site on the Equator and London, England.
Which site travels the greatest distance during one revolution (24 hours)?
Which site has the greatest speed?

6. Imagine an object launched at a
high-speed southward from London towards the equator. The object will have two
components or parts to its velocity: a high-speed southward (meridional) launch
velocity component and an eastward (zonal) velocity component due to the
rotation of Earth. Comparing London with a location on the equator, which
location has the higher eastward velocity component due to the Earth’s
rotation?

As the
object travels southward from London, it will pass over regions of Earth that
are moving faster eastward due to the rotation of Earth and the object will
appear to fall behind the rotating surface below. This means that the object
will appear to curve westward as shown in the figure (curving to the right as
viewed by someone facing the direction of the object’s motion).

7. Imagine the same object launched
northward from the Equator.
As it travels northward, it will pass over a surface that moves slower in an
eastward direction. Will the object appear to follow a straight line? Curve to
the left? Or curve to the right?

You have
studied the motion of an object launched in the Northern Hemisphere and have
seen that the object appears to curve to the right as measured by observers
rotating with Earth. You will create additional examples of motion in the
Northern Hemisphere in the following investigations and will learn that each
one follows the same rule: In the Northern Hemisphere, moving objects appear
to curve to the right on the rotating Earth.

The case
of objects launched directly eastward or westward requires special attention.
Examine the following figures to verify that in both cases the object’s
trajectory follows the same rule.

North
Pole View/Eastward
Launch

North
Pole View/Westward
Launch

Objects
launched eastward from London will appear to curve outward as you rotate
eastward with Earth.

Objects launched
westward from London will appear to curve downward as you rotate eastward
with Earth.

Westward
View/Eastward
Launch

Westward
View/Westward
Launch

In this
view, the launched object (in the small red box) is moving eastward (towards
you, out of the paper). It appears to curve outward (red arrow) as you rotate
with the Earth after the launch. The object’s apparent velocity in the plane
of the paper (red arrow) has two components: an upward (blue) component and a
southward (green) component. This southward component will cause the
eastward-moving object’s path bend southward.

It
follows the curve right rule.

In this
view, the launched object (in the small red box) is moving westward (away
from you, into the paper). It appears to curve towards the Earth’s axis (red
arrow) as you rotate with the Earth after the launch. The object’s apparent
velocity in the plane of the paper (red arrow) has two components: a downward
(blue) component and a northward (green) component. This northward component will
cause the westward-moving object’s path bend northward.

It
follows the curve right rule.

8. Imagine the same object traveling
southward from the Equator. As it moves southward, it will pass over a surface
that moves slower in an eastward direction. Will an object appear to follow a
straight line? Curve to the left? Or curve to the right?

The
general rules for moving objects on a rotating sphere are:

• In
the Northern Hemisphere, a balance of forces on the rotating Earth influences moving
objects to curve right.

• In
the Southern Hemisphere, a balance of forces on the rotating Earth influences moving
objects to curve left.

Sizing-up Inertial Circles (Oscillations)

The
equations governing the magnitude (strength) of the Coriolis force, FC,
are:

Where m
is the mass of the object, v is the horizontal component of its velocity, ω is the rotational speed of the Earth (7.27x10-5 radians/second), f is the frequency of the motion and Φ is the latitude of the moving object. Under the
influence of the Coriolis force, objects follow curved, near-circular paths,
called inertial circles. Their motions repeating patterns or inertial
oscillations that repeat with a frequency, f, during a time period T=1/f. The
radius of the Coriolis inertial circle is:

The Coriolis force
is evident in swirling vortex weather patterns (like hurricanes), leading to a counter-clockwise
rotation in the Northern Hemisphere and a clockwise rotation on the Southern Hemisphere.

An example, right, is the beautifully formed low-pressure
system swirling off the southwestern coast of Iceland. Because this
low-pressure system occurred in the Northern Hemisphere, the winds spun in
toward the center of the low-pressure system in a counter-clockwise direction.

9. Use the formulas in the
table below, to estimate the frequency of the inertial oscillations and the
size of the inertial circles at several latitudes. Do this for both air
currents (typical wind speed 10 m/s) and ocean currents (typical ocean current
0.2 m/s). Once you have found the frequency for the latitude, use that number
(f in the equation) to find the radious of the inertial circle. Compute the
missing values in the following table. Put your answers in the empty boxes
below.

Latitude

(Φ, degrees)

Frequency,
f

f=2(7.27x10-5)sin(Φ)

Current

Fluid

Speed

(m/s)

Inertial
Circle

Radius
R=v/f

(m)

20

Air

10

20

Water

.2

50

Air

10

50

Water

.2

80

Air

10

80

Water

.2

Take A
Spin With The Coriolis Model

To help
you better understand the Coriolis forces on a rotating sphere, a Coriolis
Model visualizer has been provided to simulate the motion of an object sliding without
friction on a sphere with the same size and rotational speed as Earth. The
object is allowed to slide freely for 7 days and you are allowed to set the
object’s starting velocity (speed and direction) and position.

Click on
the hypertext word Coriolis Model to open a new window containing the model. Complete the following four
trials to determine if the trajectory follows the two Coriolis
Rules—illustrated below. For each trial:

• First,
Select the object’s starting direction and starting speed from the drop down
menus.

• Second,
click on the map at a site in the hemisphere indicated in the table below.

• A
pop-up window will appear showing the trajectory of the object tracked over a
1-week time period.

10. Next, use the following table to
make your model settings. Click the map over the ocean at the correct starting
latitude and decide if the trajectory follows our curvature rules for the
Northern and Southern Hemispheres. Put your answers in the table below.

Trial

Coriolis
Model Initial Settings

Your
Analysis of the Trajectory

Starting
Speed (m/sec)

Starting
Direction

Starting
Latitude

Trajectory
Follows Rules

Direction
Trajectory Curves

1

50

North

+30o

Northern
Hemisphere

2

50

North

-30o

Southern
Hemisphere

3

50

East

+30o

Northern

Hemisphere

4

50

West

-30o

Southern

Hemisphere

Trial
1

Trial
2

Trial
3

Trial
4

11. The Equator is the dividing line
for the two rules that apply to moving objects. What might happen if an object
is launched in either hemisphere but crosses over the equator during its
trajectory?

12. To test your understanding, make
a prediction of what will happen to an object when it is launched in the manner
specified in each row of the following table. Check your predictions using the
Coriolis Accelerated Motion visualizer, and then put your answers in the
table below.

Trial

Starting

Speed (m/sec)

Starting
Direction

Starting
Location

Predicted
Trajectory

if
object crosses Equator

Does
your prediction agree or disagree with visualizer?

5

50

South

15o North

6

50

North

15 o South

7

50

East

15 o North

8

50

West

15 o South

Trial
5

Trial
6

Trial
7

Trial
8

As
discussed previously in this lesson, the trade winds are driven by heated,
light air at the Equator rising up and drawing in cooler surface air slightly
north and south of the Equator.

It should
be clear from the trajectories in trial 5 and trial 6 that air rushing towards
the Equator will curve towards the west whether the air comes from the north or
south. This creates a pattern of easterly winds (winds blowing from the east)
at the Equator. Note that the air masses from the north and south will collide
at the Equator and that interaction will strengthen the equatorial wind
pattern. The computer model you have been using models a sliding object freely
moving over a smooth Earth-sized sphere with nothing blocking its path as it
slides above or below the Equator. This is not the case for the air in the
atmosphere. The air rushing to the Equator will be driven further in the
westward direction by the converging air masses and will not significantly
cross the Equator. Tinka Sloss, NewMedia Studio,
Inc.

13. Next, use the Coriolis Model to do a study of how the Coriolis
force varies with latitude. You will use the computer model to launch objects
at various latitudes. By observing the curvature of the trajectory, you can
estimate the relative strength of the deflecting force: strongly deflecting
forces result in small, tight circular paths, weakly deflecting forces result
on large circular paths. As we have seen, these near-circular paths are called
inertial circles and the frequency of rotation, f, and the speed, v, determine
the radius of the circle:

On a
rotating planet, the frequency increases with latitude, Φ:

These
equations predict that, for constant speed, the radius of a moving object
trajectory should decrease with latitude.

14. Fill in the following table and
draw a conclusion about how the Coriolis force varies with latitude. Indicate
your estimates of radius and force, use the subjective relative scale: small/weak,
medium, or large/strong.

Note: The speed
of the object is kept constant. In this case, the radius and acceleration are
inversely proportional (large R gives a small A; small R gives a large A):

Starting
Position

Starting

Speed

(m/sec)

Starting

Direction

Radius
of Curvature

of
Trajectory

(small,
medium, large)

Coriolis
Force

(small,
medium, large)

85 N

50

East

45 N

50

East

15 N

50

East

15 S

50

East

45 S

50

East

85 S

50

East

15. What do you conclude about the
effect of latitude on the Coriolis acceleration?

Additional Investigations for the Coriolis
Force and Travel

How
does the Coriolis force impact travel on a rotating sphere?

Do airline pilots need to consider the Coriolis force when
making their flight plan?

Do ship captions need to consider the Coriolis force when
charting their course?

Matrix
for Grading Lesson 2

Proficiency Level

Description

4

Expert

Responses
show an in-depth understanding of models and explorations used to explain
scientific concepts and processes used in the lesson. Proficient manipulation
of computer models. Data collection and analysis of data are complete and
accurate. Predictions and follow through with accuracy of predictions are
explained and fully supported with relevant data and examples.

3

Proficient

Responses
show a solid understanding of models and explorations used to explain
scientific concepts and processes used in the lesson. Mostly proficient
manipulation of computer models. Data collection and analysis of data are
mostly complete and accurate. Predictions and follow through with accuracy of
predictions are explained and mostly supported with relevant data and
examples.

2

Emergent

Responses
show a partial understanding of models and explorations used to explain
scientific concepts and processes used in the lesson. Some proficiency in
manipulation of computer models. Data collection and analysis of data are
partially complete and sometimes accurate. Predictions and follow through
with accuracy of predictions are sometimes explained and supported with
relevant data and examples.

1

Novice

Responses
show a very limited understanding of models used to explain scientific
concepts and processes used in the lesson. Little or no ability shown to
manipulate computer models. Data collection and analysis of data are
partially complete and sometimes accurate. Predictions and follow through
with accuracy of predictions are not well explained and are not supported
with relevant data and examples.